Решение:

1) а) 6,83 + 7,81 + 3,17+8,19 = (6,83 + 3,17) + (7,81 + 8,19) = 10 + 16 = 26.

б) -5,37 +9,29 +4,37 = 9,29 + (4,37 - 5,37) = 9,29 - 1 = 8,29.

2) a) 527-825 +925 = 527 + (925 - 825) = 527 + 100 = 627.

б) $$7\frac{1}{4}+13\frac{7}{8}+15\frac{3}{4}+17\frac{1}{8} = (7\frac{1}{4} + 15\frac{3}{4}) + (13\frac{7}{8} + 17\frac{1}{8}) = (7 + 15 + \frac{1}{4} + \frac{3}{4}) + (13 + 17 + \frac{7}{8} + \frac{1}{8}) = (22 + \frac{4}{4}) + (30 + \frac{8}{8}) = 23 + 31 = $$ 54.

3) a) $$\frac{2}{19} \cdot 13,5 \cdot 19 = \frac{2}{19} \cdot 19 \cdot 13,5 = 2 \cdot 13,5 = $$ 27.

б) $$28 \cdot 3,9 \cdot \frac{5}{14} = 28 \cdot \frac{5}{14} \cdot 3,9 = \frac{28}{14} \cdot 5 \cdot 3,9 = 2 \cdot 5 \cdot 3,9 = 10 \cdot 3,9 =$$ 39.

4) а) $$3\frac{3}{11} \cdot \frac{21}{17} \cdot \frac{11}{3} \cdot \frac{17}{21} = \frac{3\cdot11+3}{11} \cdot \frac{21}{17} \cdot \frac{11}{3} \cdot \frac{17}{21} = \frac{36}{11} \cdot \frac{21}{17} \cdot \frac{11}{3} \cdot \frac{17}{21} = \frac{36}{3} \cdot \frac{21}{21} \cdot \frac{11}{11} \cdot \frac{17}{17} = 12 \cdot 1 \cdot 1 \cdot 1 = $$ 12.

б) $$(-\frac{7}{31}) \cdot (-\frac{2}{13}) \cdot \frac{31}{7} \cdot (-\frac{13}{20}) = (-\frac{7}{31} \cdot \frac{31}{7}) \cdot (-\frac{2}{13} \cdot -\frac{13}{20}) = -1 \cdot \frac{2}{20} = -\frac{1}{10} = $$ -0,1.